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Unit 3: Averages and VariationsWeek 6Ms. Sanchez
MODEMode: the value in a data set that occurs most frequently
5 3 7 2 4 4 3 2 4 8 3 4 3 1 2 2 1 4 5 2 3 5 2 3 5 3
1 = 22 = 6 3 = 74 = 55 = 46 = 07 = 18 = 1
MEDIANMedian: is the central value of an ordered distribution. The data set must be ordered from smallest to largest.
Odd data set: the middle data value
4 3 2 4 8 3 4 3 1 2 2
Ordered data set: 1 2 2 2 3 3 3 4 4 4 8
Median: 3
Even data set: add both middle numbers divide by 210 9 6 8 1 12 3 2
Ordered data set: 1 2 3 6 8 9 10 12
Median:
MEANMean: is the average that uses the exact value of each entry.
DATA SET
• 17• 12• 14• 17• 13• 16• 18• 20• 13
Vocabulary Terms
Sample Mean: , is the mean of the sample data set.
Population mean: is the mean of the entire population
Resistant Measure: is one that is not influenced by extremely high or low data values
Mean is NOT a resistant measure
Mode is a resistant measure
Go to Google Classroom
Work on the handout.
Use the notes you just took
This will be worth 5 stamps.
Finish it by the end of the period.
TURN IT IN!
RANGEIn arithmetic:
Is the difference between the smallest and the largest value in the data set.
In statistics:The size of the smallest interval contains all the data and provides an indicator of statistical dispersion.
EX.2 3 4 7 8 9 10 12 15 Range: 15 - 2 = 13
Standard DeviationThe standard deviation of a set of data is the average distance between the mean and the observed scores. A measure of how spread out are the numbers.
Population Standard deviation: a measure of how spread out are the numbers in the population. Normally used in a Normal Distribution.
Sample Standard deviation: a measure of how spread out are the numbers in the sample.
Finding standard deviation.
Find the sample standard deviation of the data set.
2 3 4 5 6 8 10 10
VarianceThe average of the squared differences from the mean. The standard deviation squared.
Population variance:
Sample variance:
Find the sample variance
2 3 3 5 6 8 10
Coefficient of variationA percentage of the ratio of the standard
deviation to the mean. It shows the extent of variability in relation to the mean of the population. * If a data set has a high percentage of CV then
Using population mean and population standard deviation
Using sample mean and sample standard deviation
Find the coefficient of variation
2 3 4 5 6 8 10 10
QuartilesAre a special type of percentile that divide the data into fourths:
1st quartile “Q1” is the 25th percentile
2nd quartile “Q2” is the 50th percentile (also known as the median
3rd quartile “Q3” is the 75th percentile
How to compute quartiles1. Order the data from smallest to largest
2. Find the median, this is Q2.
3. Q1 (1st quartile) is the median of the lower half of the data.• It’s the median of the data falling BELOW the
Q2. NOT including Q2
4. Q3 (3rd quartile) is the median of the upper half of the data.• It’s the median of the data falling ABOVE the
Q2. NOT including Q2.
Finding the quartilesCalories in vanilla flavored ice cream bars.
342 377 319 439 295 239 197 131 151 209 151 190
Interquartile RangeIQR = interquartile range. Is the difference between the Q3 and Q1
Q3 – Q1= IQR
5 Number Summary
Is a summary of data with the low and high data values, along with the quartiles
Low Q1 Q2 Q3 Max
BoxplotUsing the 5 number summary we can draw a diagram to represent a graphic sketch of the data collected.
Stem and leaf plotA plot where each data value is split into a leaf (the last digits) and a stem (the first digit). Data must be rearranged from smallest to largest.
32 = 3 (stem) 2 (leaf)
15 = 1 (stem) 2 leaf)
15, 16, 21 23, 23, 26, 26, 30, 32, 41
Create a stem leaf plot from the following set of
data.Sam got his friends to do a long jump and got these different results.
2.3, 2.5, 2.7, 2.8, 3.2, 3.6, 4.5, 5.0
Skewedness in stem plots & histograms
Develop a histogram from the stem leaf plot.